PI-EXCITATION OF THE T-J MODEL

In this paper, we present analytical and numerical calculations of the pi resonance in the t-J model. We show in detail how the pi resonance in the particle-particle channel couples to the dynamical spin correl ation function in a superconducting state. The contribution of the pi resonance to the spin excitation spectrum can be estimated from genera l model-independent sum rules, and it agrees with our detailed calcula tions. The results are in overall agreement with the exact diagonaliza tion studies of the t-J model. Earlier calculations predicted the corr ect doping dependence of the neutron resonance peak in the YBa2CU3O6+x superconductor, and in this paper detailed energy and momentum depend ence of the spin correlation function is presented. The microscopic eq uations of motion obtained within current formalism agree with that of the SO(5) nonlinear sigma model, where the pi resonance is interprete d as a pseudo-Goldstone mode of the spontaneous SO(5) symmetry breakin g.